Aim: This class represents an arbitrary cubical complex living in some Khalimsky space. Cubical complexes are sets of cells of different dimensions related together with incidence relations. Two cells in a cubical complex are incident if and only if they are incident in the surrounding Khalimsky space. In other words, cubical complexes are defined here as subsets of Khalimsky spaces. More...

#include <DGtal/topology/CubicalComplex.h>

Inheritance diagram for DGtal::CubicalComplex< TKSpace, TCellContainer >:

Data Structures
struct	ConstIterator

struct	DefaultCellMapIteratorPriority

struct	Iterator

Public Types
enum	CellType { Maximal , Free , Any }
	Possible cell types within a complex. More...

typedef CubicalComplex< TKSpace, TCellContainer >	Self

typedef TKSpace	KSpace
	Type of the cellular grid space. More...

typedef TCellContainer	CellContainer
	Type for storing cells, an associative container Cell -> Data. More...

typedef CellContainer::mapped_type	Data
	Type of data associated to each cell. More...

typedef KSpace::Integer	Integer
	Type for integers in the space. More...

typedef KSpace::Cell	Cell
	Type for a cell in the space. More...

typedef Cell::PreCell	PreCell
	Type for a precell in the space. More...

typedef KSpace::Cells	Cells
	Type for a sequence of cells in the space. More...

typedef KSpace::Space	Space
	Type of the digital space. More...

typedef KSpace::Size	Size
	Type for a number of elements. More...

typedef KSpace::Point	Point
	Type for a point in the digital space. More...

typedef KSpace::DirIterator	DirIterator
	Type for iterating over cell directions. More...

typedef CellContainer	CellMap
	Type for storing cells, an associative container Cell -> Data. More...

typedef CellMap::const_iterator	CellMapConstIterator
	Const iterator for visiting type CellMap. More...

typedef CellMap::iterator	CellMapIterator
	Iterator for visiting type CellMap. More...

typedef ConstIterator	const_iterator

typedef Iterator	iterator

typedef Cell	value_type

typedef Cell const &	reference

typedef Cell const &	const_reference

typedef CellContainer::size_type	size_type

typedef CellContainer::difference_type	difference_type

typedef Cell const *	pointer

typedef Cell const *	const_pointer

Public Member Functions
	BOOST_CONCEPT_ASSERT ((concepts::CCellularGridSpaceND< TKSpace >))

	BOOST_STATIC_ASSERT (IsPairAssociativeContainer< TCellContainer >::value)

	BOOST_CONCEPT_ASSERT ((concepts::CSTLAssociativeContainer< TCellContainer >))

	BOOST_STATIC_ASSERT ((boost::is_base_of< CubicalCellData, Data >::value))

	BOOST_STATIC_ASSERT ((boost::is_same< typename TKSpace::Cell, typename CellContainer::key_type >::value))

	BOOST_STATIC_CONSTANT (uint32_t, REMOVED=0x10000000)
	Flag Used to indicate in a cell data that this cell has been (virtually) removed. More...

	BOOST_STATIC_CONSTANT (uint32_t, COLLAPSIBLE=0x20000000)
	Flag Used to indicate in a cell data that this cell is collapsible. More...

	BOOST_STATIC_CONSTANT (uint32_t, FIXED=0x40000000)
	Flag Used to indicate in a cell data that this cell is fixed. More...

	BOOST_STATIC_CONSTANT (uint32_t, USER1=0x80000000)
	User flag for a cell. More...

	BOOST_STATIC_CONSTANT (uint32_t, VALUE=0x0fffffff)
	Value for a cell. More...

	~CubicalComplex ()

	CubicalComplex (ConstAlias< KSpace > aK)

	CubicalComplex (const CubicalComplex &other)

template<typename TDigitalSet >
void	construct (const TDigitalSet &set)

CubicalComplex &	operator= (const CubicalComplex &other)

void	clear ()

void	clear (Dimension d)

void	fillData (Data data=Data())

void	fillData (Dimension d, Data data=Data())

Dimension	dim () const

Dimension	dim (const Cell &aCell) const

Size	nbCells (Dimension d) const

Integer	euler () const

const KSpace &	space () const

const CellMap &	getCells (const Dimension d) const

CellMap &	getCells (const Dimension d)

ConstIterator	begin () const

ConstIterator	end () const

Iterator	begin ()

Iterator	end ()

Size	count (const Cell &aCell) const

Size	size () const

Size	max_size () const

bool	empty () const

std::pair< ConstIterator, ConstIterator >	equal_range (const Cell &aCell) const

std::pair< Iterator, Iterator >	equal_range (const Cell &aCell)

void	erase (Iterator position)

Size	erase (const Cell &aCell)

void	erase (Iterator first, Iterator last)

ConstIterator	find (const Cell &aCell) const

Iterator	find (const Cell &aCell)

std::pair< Iterator, bool >	insert (const Cell &aCell)

Iterator	insert (Iterator position, const Cell &aCell)

template<class InputIterator >
void	insert (InputIterator first, InputIterator last)

void	swap (CubicalComplex &other)

Data &	operator[] (const Cell &aCell)

bool	operator() (const Cell &aCell) const

void	insertCell (const Cell &aCell, const Data &data=Data())

void	insertCell (Dimension d, const Cell &aCell, const Data &data=Data())

template<typename CellConstIterator >
void	insertCells (CellConstIterator it, CellConstIterator itE, const Data &data=Data())

template<typename CellConstIterator >
void	insertCells (Dimension d, CellConstIterator it, CellConstIterator itE, const Data &data=Data())

bool	belongs (const Cell &aCell) const

bool	belongs (const PreCell &aCell) const

bool	belongs (Dimension d, const Cell &aCell) const

bool	belongs (Dimension d, const PreCell &aCell) const

Size	eraseCell (const Cell &aCell)

Size	eraseCell (Dimension d, const Cell &aCell)

void	eraseCell (CellMapIterator it)

void	eraseCells (CellMapIterator it, CellMapIterator itE)

template<typename CellConstIterator >
Size	eraseCells (CellConstIterator it, CellConstIterator itE)

template<typename CellConstIterator >
Size	eraseCells (Dimension d, CellConstIterator it, CellConstIterator itE)

template<typename CellOutputIterator >
void	faces (CellOutputIterator &outIt, const Cell &aCell, bool hintClosed=false) const

template<typename CellOutputIterator >
void	directFaces (CellOutputIterator &outIt, const Cell &aCell, bool hintClosed=false) const

template<typename CellMapIteratorOutputIterator >
void	directFacesIterators (CellMapIteratorOutputIterator &outIt, const Cell &aCell)

template<typename CellOutputIterator >
void	coFaces (CellOutputIterator &outIt, const Cell &aCell, bool hintOpen=false) const

template<typename CellOutputIterator >
void	directCoFaces (CellOutputIterator &outIt, const Cell &aCell, bool hintOpen=false) const

template<typename CellMapIteratorOutputIterator >
void	directCoFacesIterators (CellMapIteratorOutputIterator &outIt, const Cell &aCell)

CellMapConstIterator	begin (Dimension d) const

CellMapConstIterator	end (Dimension d) const

CellMapIterator	begin (Dimension d)

CellMapIterator	end (Dimension d)

CellMapConstIterator	findCell (const Cell &aCell) const

CellMapConstIterator	findCell (Dimension d, const Cell &aCell) const

CellMapIterator	findCell (const Cell &aCell)

CellMapIterator	findCell (Dimension d, const Cell &aCell)

Cells	cellBoundary (const Cell &aCell, bool hintClosed=false) const

Cells	cellCoBoundary (const Cell &aCell, bool hintOpen=false) const

bool	isCellInterior (const Cell &aCell) const

bool	isCellBoundary (const Cell &aCell) const

CellType	computeCellType (const Cell &c, CellMapIterator &it_cell_up, Dimension n=dimension)

CubicalComplex	interior () const

CubicalComplex	boundary (bool hintClosed=false) const

void	getInteriorAndBoundary (CubicalComplex &intcc, CubicalComplex &bdcc, bool hintClosed=false) const

CubicalComplex	closure (const CubicalComplex &S, bool hintClosed=false) const

CubicalComplex	star (const CubicalComplex &S, bool hintOpen=false) const

CubicalComplex	link (const CubicalComplex &S, bool hintClosed=false, bool hintOpen=false) const

void	close ()

void	close (Dimension k)

void	open ()

void	open (Dimension k)

void	selfDisplay (std::ostream &out) const

bool	isValid () const

std::string	className () const

Static Public Attributes
static const Dimension	dimension = KSpace::dimension
	The dimension of the embedding space. More...

Protected Member Functions
	CubicalComplex ()

Protected Attributes
const KSpace *	myKSpace
	The Khalimsky space in which lives the cubical complex. More...

std::vector< CellMap >	myCells

Friends
template<typename K , typename C >
CubicalComplex< K, C > &	DGtal::operator\|= (CubicalComplex< K, C > &, const CubicalComplex< K, C > &)

template<typename K , typename C >
CubicalComplex< K, C > &	DGtal::operator&= (CubicalComplex< K, C > &, const CubicalComplex< K, C > &)

template<typename K , typename C >
CubicalComplex< K, C > &	DGtal::operator^= (CubicalComplex< K, C > &, const CubicalComplex< K, C > &)

template<typename K , typename C >
CubicalComplex< K, C > &	DGtal::operator-= (CubicalComplex< K, C > &, const CubicalComplex< K, C > &)

template<typename K , typename C >
CubicalComplex< K, C >	DGtal::operator\| (const CubicalComplex< K, C > &, const CubicalComplex< K, C > &)

template<typename K , typename C >
CubicalComplex< K, C >	DGtal::operator& (const CubicalComplex< K, C > &, const CubicalComplex< K, C > &)

template<typename K , typename C >
CubicalComplex< K, C >	DGtal::operator^ (const CubicalComplex< K, C > &, const CubicalComplex< K, C > &)

template<typename K , typename C >
CubicalComplex< K, C >	DGtal::operator- (const CubicalComplex< K, C > &, const CubicalComplex< K, C > &)

template<typename K , typename C >
CubicalComplex< K, C >	DGtal::operator~ (const CubicalComplex< K, C > &)

template<typename K , typename C >
CubicalComplex< K, C >	DGtal::operator* (const CubicalComplex< K, C > &)

template<typename K , typename C >
bool	DGtal::operator== (const CubicalComplex< K, C > &, const CubicalComplex< K, C > &)

template<typename K , typename C >
bool	DGtal::operator!= (const CubicalComplex< K, C > &, const CubicalComplex< K, C > &)

template<typename K , typename C >
bool	DGtal::operator<= (const CubicalComplex< K, C > &, const CubicalComplex< K, C > &)

template<typename K , typename C >
bool	DGtal::operator>= (const CubicalComplex< K, C > &, const CubicalComplex< K, C > &)

Detailed Description

template<typename TKSpace, typename TCellContainer = typename TKSpace::template CellMap< CubicalCellData >::Type>
class DGtal::CubicalComplex< TKSpace, TCellContainer >

Aim: This class represents an arbitrary cubical complex living in some Khalimsky space. Cubical complexes are sets of cells of different dimensions related together with incidence relations. Two cells in a cubical complex are incident if and only if they are incident in the surrounding Khalimsky space. In other words, cubical complexes are defined here as subsets of Khalimsky spaces.

Description of template class 'CubicalComplex'

A cubical complex is a (immutable) model of boost::Container and offers forward iterators to enumerate elements. It is close from being an AssociativeContainer, but values are not sorted (they are sorted per dimension), and are not modifiable. It is not exactly a container in the usual sense because it cannot be constructed by default, and because iterators may not modified values.

Template Parameters

TKSpace	any model of concepts::CCellularGridSpaceND, i.e. a type that models a Khalimsky space.
TCellContainer	any model of associative container, mapping a KSpace::Cell to a CubicalCellData or any type deriving from it. It could be for instance a std::map or a std::unordered_map. Note that unfortunately, unordered_map are (strangely) not models of boost::AssociativeContainer, hence we cannot check concepts here.

Examples: topology/cubical-complex-collapse.cpp, topology/cubical-complex-illustrations.cpp, and topology/digitalSetToCubicalComplexes2D.cpp.

Definition at line 175 of file CubicalComplex.h.

Member Typedef Documentation

◆ Cell

template<typename TKSpace , typename TCellContainer = typename TKSpace::template CellMap< CubicalCellData >::Type>

typedef KSpace::Cell DGtal::CubicalComplex< TKSpace, TCellContainer >::Cell

Type for a cell in the space.

Definition at line 244 of file CubicalComplex.h.

◆ CellContainer

template<typename TKSpace , typename TCellContainer = typename TKSpace::template CellMap< CubicalCellData >::Type>

typedef TCellContainer DGtal::CubicalComplex< TKSpace, TCellContainer >::CellContainer

Type for storing cells, an associative container Cell -> Data.

Definition at line 234 of file CubicalComplex.h.

◆ CellMap

template<typename TKSpace , typename TCellContainer = typename TKSpace::template CellMap< CubicalCellData >::Type>

typedef CellContainer DGtal::CubicalComplex< TKSpace, TCellContainer >::CellMap

Type for storing cells, an associative container Cell -> Data.

Definition at line 251 of file CubicalComplex.h.

◆ CellMapConstIterator

template<typename TKSpace , typename TCellContainer = typename TKSpace::template CellMap< CubicalCellData >::Type>

typedef CellMap::const_iterator DGtal::CubicalComplex< TKSpace, TCellContainer >::CellMapConstIterator

Const iterator for visiting type CellMap.

Definition at line 252 of file CubicalComplex.h.

◆ CellMapIterator

template<typename TKSpace , typename TCellContainer = typename TKSpace::template CellMap< CubicalCellData >::Type>

typedef CellMap::iterator DGtal::CubicalComplex< TKSpace, TCellContainer >::CellMapIterator

Iterator for visiting type CellMap.

Definition at line 253 of file CubicalComplex.h.

◆ Cells

template<typename TKSpace , typename TCellContainer = typename TKSpace::template CellMap< CubicalCellData >::Type>

typedef KSpace::Cells DGtal::CubicalComplex< TKSpace, TCellContainer >::Cells

Type for a sequence of cells in the space.

Definition at line 246 of file CubicalComplex.h.

◆ const_iterator

template<typename TKSpace , typename TCellContainer = typename TKSpace::template CellMap< CubicalCellData >::Type>

typedef ConstIterator DGtal::CubicalComplex< TKSpace, TCellContainer >::const_iterator

Definition at line 514 of file CubicalComplex.h.

◆ const_pointer

template<typename TKSpace , typename TCellContainer = typename TKSpace::template CellMap< CubicalCellData >::Type>

typedef Cell const* DGtal::CubicalComplex< TKSpace, TCellContainer >::const_pointer

Definition at line 522 of file CubicalComplex.h.

◆ const_reference

template<typename TKSpace , typename TCellContainer = typename TKSpace::template CellMap< CubicalCellData >::Type>

typedef Cell const& DGtal::CubicalComplex< TKSpace, TCellContainer >::const_reference

Definition at line 518 of file CubicalComplex.h.

◆ Data

template<typename TKSpace , typename TCellContainer = typename TKSpace::template CellMap< CubicalCellData >::Type>

typedef CellContainer::mapped_type DGtal::CubicalComplex< TKSpace, TCellContainer >::Data

Type of data associated to each cell.

Definition at line 235 of file CubicalComplex.h.

◆ difference_type

template<typename TKSpace , typename TCellContainer = typename TKSpace::template CellMap< CubicalCellData >::Type>

typedef CellContainer::difference_type DGtal::CubicalComplex< TKSpace, TCellContainer >::difference_type

Definition at line 520 of file CubicalComplex.h.

◆ DirIterator

template<typename TKSpace , typename TCellContainer = typename TKSpace::template CellMap< CubicalCellData >::Type>

typedef KSpace::DirIterator DGtal::CubicalComplex< TKSpace, TCellContainer >::DirIterator

Type for iterating over cell directions.

Definition at line 250 of file CubicalComplex.h.

◆ Integer

template<typename TKSpace , typename TCellContainer = typename TKSpace::template CellMap< CubicalCellData >::Type>

typedef KSpace::Integer DGtal::CubicalComplex< TKSpace, TCellContainer >::Integer

Type for integers in the space.

Definition at line 243 of file CubicalComplex.h.

◆ iterator

template<typename TKSpace , typename TCellContainer = typename TKSpace::template CellMap< CubicalCellData >::Type>

typedef Iterator DGtal::CubicalComplex< TKSpace, TCellContainer >::iterator

Definition at line 515 of file CubicalComplex.h.

◆ KSpace

template<typename TKSpace , typename TCellContainer = typename TKSpace::template CellMap< CubicalCellData >::Type>

typedef TKSpace DGtal::CubicalComplex< TKSpace, TCellContainer >::KSpace

Type of the cellular grid space.

Definition at line 233 of file CubicalComplex.h.

◆ Point

template<typename TKSpace , typename TCellContainer = typename TKSpace::template CellMap< CubicalCellData >::Type>

typedef KSpace::Point DGtal::CubicalComplex< TKSpace, TCellContainer >::Point

Type for a point in the digital space.

Definition at line 249 of file CubicalComplex.h.

◆ pointer

template<typename TKSpace , typename TCellContainer = typename TKSpace::template CellMap< CubicalCellData >::Type>

typedef Cell const* DGtal::CubicalComplex< TKSpace, TCellContainer >::pointer

Definition at line 521 of file CubicalComplex.h.

◆ PreCell

template<typename TKSpace , typename TCellContainer = typename TKSpace::template CellMap< CubicalCellData >::Type>

typedef Cell::PreCell DGtal::CubicalComplex< TKSpace, TCellContainer >::PreCell

Type for a precell in the space.

Definition at line 245 of file CubicalComplex.h.

◆ reference

template<typename TKSpace , typename TCellContainer = typename TKSpace::template CellMap< CubicalCellData >::Type>

typedef Cell const& DGtal::CubicalComplex< TKSpace, TCellContainer >::reference

Definition at line 517 of file CubicalComplex.h.

◆ Self

template<typename TKSpace , typename TCellContainer = typename TKSpace::template CellMap< CubicalCellData >::Type>

typedef CubicalComplex< TKSpace, TCellContainer > DGtal::CubicalComplex< TKSpace, TCellContainer >::Self

Definition at line 179 of file CubicalComplex.h.

◆ Size

template<typename TKSpace , typename TCellContainer = typename TKSpace::template CellMap< CubicalCellData >::Type>

typedef KSpace::Size DGtal::CubicalComplex< TKSpace, TCellContainer >::Size

Type for a number of elements.

Definition at line 248 of file CubicalComplex.h.

◆ size_type

template<typename TKSpace , typename TCellContainer = typename TKSpace::template CellMap< CubicalCellData >::Type>

typedef CellContainer::size_type DGtal::CubicalComplex< TKSpace, TCellContainer >::size_type

Definition at line 519 of file CubicalComplex.h.

◆ Space

template<typename TKSpace , typename TCellContainer = typename TKSpace::template CellMap< CubicalCellData >::Type>

typedef KSpace::Space DGtal::CubicalComplex< TKSpace, TCellContainer >::Space

Type of the digital space.

Definition at line 247 of file CubicalComplex.h.

◆ value_type

template<typename TKSpace , typename TCellContainer = typename TKSpace::template CellMap< CubicalCellData >::Type>

typedef Cell DGtal::CubicalComplex< TKSpace, TCellContainer >::value_type

Definition at line 516 of file CubicalComplex.h.

Member Enumeration Documentation

◆ CellType

template<typename TKSpace , typename TCellContainer = typename TKSpace::template CellMap< CubicalCellData >::Type>

enum DGtal::CubicalComplex::CellType

Possible cell types within a complex.

Enumerator
Maximal	The cell has no proper coface
Free	The cell has 1 proper coface
Any	The cell has strictly more than 2 proper cofaces.

Definition at line 257 of file CubicalComplex.h.

                  {
      Maximal ,
      Free    ,
      Any     
    };

Constructor & Destructor Documentation

◆ ~CubicalComplex()

template<typename TKSpace , typename TCellContainer = typename TKSpace::template CellMap< CubicalCellData >::Type>

DGtal::CubicalComplex< TKSpace, TCellContainer >::~CubicalComplex ( )

Destructor.

◆ CubicalComplex() [1/3]

template<typename TKSpace , typename TCellContainer = typename TKSpace::template CellMap< CubicalCellData >::Type>

DGtal::CubicalComplex< TKSpace, TCellContainer >::CubicalComplex ( )

protected

Constructor. The cubical complex is not valid. A user may not instantiate an empty CubicalComplex, because it needs the Khalimsky space.

◆ CubicalComplex() [2/3]

template<typename TKSpace , typename TCellContainer = typename TKSpace::template CellMap< CubicalCellData >::Type>

DGtal::CubicalComplex< TKSpace, TCellContainer >::CubicalComplex ( ConstAlias< KSpace > aK )

Constructor of empty complex. Needs a space to represents cubical cells.

Parameters

aK	a Khalimsky space.

◆ CubicalComplex() [3/3]

template<typename TKSpace , typename TCellContainer = typename TKSpace::template CellMap< CubicalCellData >::Type>

DGtal::CubicalComplex< TKSpace, TCellContainer >::CubicalComplex ( const CubicalComplex< TKSpace, TCellContainer > & other )

Copy constructor.

Parameters

other the object to clone.

Member Function Documentation

◆ begin() [1/4]

template<typename TKSpace , typename TCellContainer = typename TKSpace::template CellMap< CubicalCellData >::Type>

Iterator DGtal::CubicalComplex< TKSpace, TCellContainer >::begin ( )

Returns: an iterator pointing on the first cell of this complex (lower dimensional cells come first).

◆ begin() [2/4]

template<typename TKSpace , typename TCellContainer = typename TKSpace::template CellMap< CubicalCellData >::Type>

ConstIterator DGtal::CubicalComplex< TKSpace, TCellContainer >::begin ( ) const

Returns: an iterator pointing on the first cell of this complex (lower dimensional cells come first).

Referenced by DGtal::CubicalComplex< TKSpace, TCellContainer >::ConstIterator::ConstIterator(), drawComplex(), GIVEN(), DGtal::CubicalComplex< TKSpace, TCellContainer >::Iterator::Iterator(), main(), DGtal::CubicalComplex< TKSpace, TCellContainer >::ConstIterator::nextDimension(), DGtal::CubicalComplex< TKSpace, TCellContainer >::Iterator::nextDimension(), and SCENARIO().

◆ begin() [3/4]

template<typename TKSpace , typename TCellContainer = typename TKSpace::template CellMap< CubicalCellData >::Type>

CellMapIterator DGtal::CubicalComplex< TKSpace, TCellContainer >::begin ( Dimension d )

Parameters

d	any valid dimension.

Returns: an iterator pointing on the first cell of dimension d of this.

◆ begin() [4/4]

template<typename TKSpace , typename TCellContainer = typename TKSpace::template CellMap< CubicalCellData >::Type>

CellMapConstIterator DGtal::CubicalComplex< TKSpace, TCellContainer >::begin ( Dimension d ) const

Parameters

d	any valid dimension.

Returns: a const iterator pointing on the first cell of dimension d of this.

◆ belongs() [1/4]

template<typename TKSpace , typename TCellContainer = typename TKSpace::template CellMap< CubicalCellData >::Type>

bool DGtal::CubicalComplex< TKSpace, TCellContainer >::belongs ( const Cell & aCell ) const

Parameters

aCell any cell valid in the Khalimsky space associated to the complex.

Returns: 'true' if and only if aCell belongs to this complex.

◆ belongs() [2/4]

template<typename TKSpace , typename TCellContainer = typename TKSpace::template CellMap< CubicalCellData >::Type>

bool DGtal::CubicalComplex< TKSpace, TCellContainer >::belongs ( const PreCell & aCell ) const

Parameters

aCell any pre-cell valid in the Khalimsky space associated to the complex.

Returns: 'true' if and only if aCell belongs to this complex.

◆ belongs() [3/4]

template<typename TKSpace , typename TCellContainer = typename TKSpace::template CellMap< CubicalCellData >::Type>

bool DGtal::CubicalComplex< TKSpace, TCellContainer >::belongs	(	Dimension	d,
		const Cell &	aCell
	)		const

Parameters

d	the dimension of cell aCell.
aCell	any cell valid in the Khalimsky space associated to the complex.

Returns: 'true' if and only if aCell belongs to this complex.

◆ belongs() [4/4]

template<typename TKSpace , typename TCellContainer = typename TKSpace::template CellMap< CubicalCellData >::Type>

bool DGtal::CubicalComplex< TKSpace, TCellContainer >::belongs	(	Dimension	d,
		const PreCell &	aCell
	)		const

Parameters

d	the dimension of cell aCell.
aCell	any precell valid in the Khalimsky space associated to the complex.

Returns: 'true' if and only if aCell belongs to this complex.

◆ BOOST_CONCEPT_ASSERT() [1/2]

template<typename TKSpace , typename TCellContainer = typename TKSpace::template CellMap< CubicalCellData >::Type>

DGtal::CubicalComplex< TKSpace, TCellContainer >::BOOST_CONCEPT_ASSERT ( (concepts::CCellularGridSpaceND< TKSpace >) )

◆ BOOST_CONCEPT_ASSERT() [2/2]

template<typename TKSpace , typename TCellContainer = typename TKSpace::template CellMap< CubicalCellData >::Type>

DGtal::CubicalComplex< TKSpace, TCellContainer >::BOOST_CONCEPT_ASSERT ( (concepts::CSTLAssociativeContainer< TCellContainer >) )

◆ BOOST_STATIC_ASSERT() [1/3]

template<typename TKSpace , typename TCellContainer = typename TKSpace::template CellMap< CubicalCellData >::Type>

DGtal::CubicalComplex< TKSpace, TCellContainer >::BOOST_STATIC_ASSERT ( (boost::is_base_of< CubicalCellData, Data >::value) )

◆ BOOST_STATIC_ASSERT() [2/3]

template<typename TKSpace , typename TCellContainer = typename TKSpace::template CellMap< CubicalCellData >::Type>

DGtal::CubicalComplex< TKSpace, TCellContainer >::BOOST_STATIC_ASSERT ( (boost::is_same< typename TKSpace::Cell, typename CellContainer::key_type >::value) )

◆ BOOST_STATIC_ASSERT() [3/3]

template<typename TKSpace , typename TCellContainer = typename TKSpace::template CellMap< CubicalCellData >::Type>

DGtal::CubicalComplex< TKSpace, TCellContainer >::BOOST_STATIC_ASSERT ( IsPairAssociativeContainer< TCellContainer >::value )

◆ BOOST_STATIC_CONSTANT() [1/5]

template<typename TKSpace , typename TCellContainer = typename TKSpace::template CellMap< CubicalCellData >::Type>

DGtal::CubicalComplex< TKSpace, TCellContainer >::BOOST_STATIC_CONSTANT	(	uint32_t	,
		COLLAPSIBLE	= `0x20000000`
	)

Flag Used to indicate in a cell data that this cell is collapsible.

◆ BOOST_STATIC_CONSTANT() [2/5]

template<typename TKSpace , typename TCellContainer = typename TKSpace::template CellMap< CubicalCellData >::Type>

DGtal::CubicalComplex< TKSpace, TCellContainer >::BOOST_STATIC_CONSTANT	(	uint32_t	,
		FIXED	= `0x40000000`
	)

Flag Used to indicate in a cell data that this cell is fixed.

◆ BOOST_STATIC_CONSTANT() [3/5]

template<typename TKSpace , typename TCellContainer = typename TKSpace::template CellMap< CubicalCellData >::Type>

DGtal::CubicalComplex< TKSpace, TCellContainer >::BOOST_STATIC_CONSTANT	(	uint32_t	,
		REMOVED	= `0x10000000`
	)

Flag Used to indicate in a cell data that this cell has been (virtually) removed.

◆ BOOST_STATIC_CONSTANT() [4/5]

template<typename TKSpace , typename TCellContainer = typename TKSpace::template CellMap< CubicalCellData >::Type>

DGtal::CubicalComplex< TKSpace, TCellContainer >::BOOST_STATIC_CONSTANT	(	uint32_t	,
		USER1	= `0x80000000`
	)

User flag for a cell.

◆ BOOST_STATIC_CONSTANT() [5/5]

template<typename TKSpace , typename TCellContainer = typename TKSpace::template CellMap< CubicalCellData >::Type>

DGtal::CubicalComplex< TKSpace, TCellContainer >::BOOST_STATIC_CONSTANT	(	uint32_t	,
		VALUE	= `0x0fffffff`
	)

Value for a cell.

◆ boundary()

template<typename TKSpace , typename TCellContainer = typename TKSpace::template CellMap< CubicalCellData >::Type>

CubicalComplex DGtal::CubicalComplex< TKSpace, TCellContainer >::boundary ( bool hintClosed = false ) const

Computes the (topological) boundary of this complex (say X), hence it may not be a subcomplex of X, but it is a subcomplex of Cl(X).

Parameters

hintClosed when 'true', this hint tells that the complex is closed, so this speeds up this method, otherwise, the complex may be arbitrary.

Returns: the subcomplex of this composed of its boundary cells.

Referenced by main(), and SCENARIO().

◆ cellBoundary()

template<typename TKSpace , typename TCellContainer = typename TKSpace::template CellMap< CubicalCellData >::Type>

Cells DGtal::CubicalComplex< TKSpace, TCellContainer >::cellBoundary	(	const Cell &	aCell,
		bool	hintClosed = `false`
	)		const

Returns the boundary of the cell aCell as a cell collection, i.e. all the cells that are proper faces of aCell. Generally faster than method faces, which outputs cells with an output iterator.

Parameters

aCell	any cell valid in the Khalimsky space associated to the complex.
hintClosed	when 'true', this hint tells that the complex is (locally) closed, so this speeds up this method, otherwise, the complex may be arbitrary.

Returns: the collection of cells that defines the boundary of aCell, i.e. its proper faces.

Note: all returned cells belong to this complex, while it is not compulsory for aCell to belong to it.

Referenced by GIVEN().

◆ cellCoBoundary()

template<typename TKSpace , typename TCellContainer = typename TKSpace::template CellMap< CubicalCellData >::Type>

Cells DGtal::CubicalComplex< TKSpace, TCellContainer >::cellCoBoundary	(	const Cell &	aCell,
		bool	hintOpen = `false`
	)		const

Returns the co-boundary of the cell aCell as a cell collection, i.e. all the cells that are proper co-faces of aCell. Generally faster than method coFaces, which outputs cells with an output iterator.

Parameters

aCell	any cell valid in the Khalimsky space associated to the complex.
hintOpen	when 'true', this hint tells that the complex is (locally) open, so this speeds up this method, otherwise, the complex may be arbitrary.

Returns: the collection of cells that defines the co-boundary of aCell, i.e. its proper co-faces.

Note: all returned cells belong to this complex, while it is not compulsory for aCell to belong to it.

◆ className()

template<typename TKSpace , typename TCellContainer = typename TKSpace::template CellMap< CubicalCellData >::Type>

std::string DGtal::CubicalComplex< TKSpace, TCellContainer >::className ( ) const

Returns: the style name used for drawing this object.

Referenced by main().

◆ clear() [1/2]

template<typename TKSpace , typename TCellContainer = typename TKSpace::template CellMap< CubicalCellData >::Type>

void DGtal::CubicalComplex< TKSpace, TCellContainer >::clear ( )

Clears the cubical complex, which becomes empty.

Referenced by getComplex().

◆ clear() [2/2]

template<typename TKSpace , typename TCellContainer = typename TKSpace::template CellMap< CubicalCellData >::Type>

void DGtal::CubicalComplex< TKSpace, TCellContainer >::clear ( Dimension d )

Clears all cells of dimension d of the cubical complex.

Parameters

d	the dimension of cell aCell.

◆ close() [1/2]

template<typename TKSpace , typename TCellContainer = typename TKSpace::template CellMap< CubicalCellData >::Type>

void DGtal::CubicalComplex< TKSpace, TCellContainer >::close ( )

Close the whole complex (see also DGtal::operator~).

Referenced by GIVEN(), main(), DGtal::operator~(), and SCENARIO().

◆ close() [2/2]

template<typename TKSpace , typename TCellContainer = typename TKSpace::template CellMap< CubicalCellData >::Type>

void DGtal::CubicalComplex< TKSpace, TCellContainer >::close ( Dimension k )

Close all cells of dimension less or equal to k.

Parameters

k	any strictly positive integer.

◆ closure()

template<typename TKSpace , typename TCellContainer = typename TKSpace::template CellMap< CubicalCellData >::Type>

CubicalComplex DGtal::CubicalComplex< TKSpace, TCellContainer >::closure	(	const CubicalComplex< TKSpace, TCellContainer > &	S,
		bool	hintClosed = `false`
	)		const

Returns the closure of the cells in S within this complex, i.e. the smallest subcomplex that contains each cell in S.

Parameters

S	any complex the cells of which belong to this complex.
hintClosed	when 'true', this hint tells that the complex is (locally around S) closed, so this speeds up this method, otherwise, the complex may be arbitrary.

Returns: the closure of S within this complex as a cubical complex.

Referenced by main().

◆ coFaces()

template<typename TKSpace , typename TCellContainer = typename TKSpace::template CellMap< CubicalCellData >::Type>

template<typename CellOutputIterator >

void DGtal::CubicalComplex< TKSpace, TCellContainer >::coFaces	(	CellOutputIterator &	outIt,
		const Cell &	aCell,
		bool	hintOpen = `false`
	)		const

Outputs all the cells that are proper co-faces of aCell with output iterator it.

Parameters

outIt	the output iterator on Cell that is used for outputing faces.
aCell	any cell valid in the Khalimsky space associated to the complex.
hintOpen	when 'true', this hint tells that the complex is open, so this speeds up this method, otherwise, the complex may be arbitrary.

Template Parameters

CellOutputIterator any model of boost::OutputIterator, with value_type Cell.

Note: all returned cells belong to this complex, while it is not compulsory for aCell to belong to it.

◆ computeCellType()

template<typename TKSpace , typename TCellContainer = typename TKSpace::template CellMap< CubicalCellData >::Type>

CellType DGtal::CubicalComplex< TKSpace, TCellContainer >::computeCellType	(	const Cell &	c,
		CellMapIterator &	it_cell_up,
		Dimension	n = `dimension`
	)

Given a cell [c], tells if it is a maximal cell in the complex (return 0), or if it is a free face of the cell pointed by [it_cell_up] (return 1) or if it is not a free face.

The complex must be closed. In computing the 1-up-incident cells, this method ignores cell marked as REMOVED. Furthermore, if one 1-up-incident cell is not marked as COLLAPSIBLE, the method returns 2.

Parameters

[in]	c	a cubical cell (belonging to 'this')
[out]	it_cell_up	(returns) a pointer on a cell d if c is a free face of d.
[in]	n	the maximal dimension of a cell in this complex. Default to dimension, but can be less in some cases: for instance, you know that your subcomplex is a digital surface in Z3, hence you can pass 2 for n.

Returns: CellType::Maximal if the cell is maximal, CellType::Free if the cell is a free face, CellType::Any otherwise.

◆ construct()

template<typename TKSpace , typename TCellContainer = typename TKSpace::template CellMap< CubicalCellData >::Type>

template<typename TDigitalSet >

void DGtal::CubicalComplex< TKSpace, TCellContainer >::construct ( const TDigitalSet & set )

Construct a complex from a digital set.

Template Parameters

TDigitalSet either kind of DigitalSet

Parameters

set	- a digital set from which to create a complex. Set has to be of the same dimension as a Khalimsky space.

Referenced by getComplex(), and main().

◆ count()

template<typename TKSpace , typename TCellContainer = typename TKSpace::template CellMap< CubicalCellData >::Type>

Size DGtal::CubicalComplex< TKSpace, TCellContainer >::count ( const Cell & aCell ) const

Parameters

aCell any cell.

Returns: the number of matches for aCell, which is thus zero (not present) or one (present).

◆ dim() [1/2]

template<typename TKSpace , typename TCellContainer = typename TKSpace::template CellMap< CubicalCellData >::Type>

Dimension DGtal::CubicalComplex< TKSpace, TCellContainer >::dim ( ) const

Returns: the maximal dimension of a cell in the complex, 0 if the complex is empty.

◆ dim() [2/2]

template<typename TKSpace , typename TCellContainer = typename TKSpace::template CellMap< CubicalCellData >::Type>

Dimension DGtal::CubicalComplex< TKSpace, TCellContainer >::dim ( const Cell & aCell ) const

Parameters

aCell any cell valid in the Khalimsky space associated to the complex.

Returns: the dimension of the cell aCell.

◆ directCoFaces()

template<typename TKSpace , typename TCellContainer = typename TKSpace::template CellMap< CubicalCellData >::Type>

template<typename CellOutputIterator >

void DGtal::CubicalComplex< TKSpace, TCellContainer >::directCoFaces	(	CellOutputIterator &	outIt,
		const Cell &	aCell,
		bool	hintOpen = `false`
	)		const

Outputs all the cells that are direct co-faces of aCell with output iterator it (direct faces are upper incident cells with a dimension just one above).

Parameters

outIt	the output iterator on Cell that is used for outputing faces.
aCell	any cell valid in the Khalimsky space associated to the complex.
hintOpen	when 'true', this hint tells that the complex is open, so this speeds up this method, otherwise, the complex may be arbitrary.

Template Parameters

CellOutputIterator any model of boost::OutputIterator, with value_type Cell.

Note: all returned cells belong to this complex, while it is not compulsory for aCell to belong to it.

Referenced by GIVEN().

◆ directCoFacesIterators()

template<typename TKSpace , typename TCellContainer = typename TKSpace::template CellMap< CubicalCellData >::Type>

template<typename CellMapIteratorOutputIterator >

void DGtal::CubicalComplex< TKSpace, TCellContainer >::directCoFacesIterators	(	CellMapIteratorOutputIterator &	outIt,
		const Cell &	aCell
	)

Outputs all the iterators on cells that are direct co-faces of aCell with output iterator it (direct faces are upper incident cells with a dimension just one above).

Parameters

outIt	the output iterator on CellMapIterator that is used for outputing face iterators.
aCell	any cell valid in the Khalimsky space associated to the complex.

Template Parameters

CellMapIteratorOutputIterator any model of boost::OutputIterator, with value_type CellMapIterator.

Note: all returned cells belong to this complex, while it is not compulsory for aCell to belong to it.

◆ directFaces()

template<typename TKSpace , typename TCellContainer = typename TKSpace::template CellMap< CubicalCellData >::Type>

template<typename CellOutputIterator >

void DGtal::CubicalComplex< TKSpace, TCellContainer >::directFaces	(	CellOutputIterator &	outIt,
		const Cell &	aCell,
		bool	hintClosed = `false`
	)		const

Outputs all the cells that are direct faces of aCell with output iterator it (direct faces are lower incident cells with a dimension just one below).

Parameters

outIt	the output iterator on Cell that is used for outputing faces.
aCell	any cell valid in the Khalimsky space associated to the complex.
hintClosed	when 'true', this hint tells that the complex is closed, so this speeds up this method, otherwise, the complex may be arbitrary.

Template Parameters

CellOutputIterator any model of boost::OutputIterator, with value_type Cell.

Note: all returned cells belong to this complex, while it is not compulsory for aCell to belong to it.

Referenced by GIVEN().

◆ directFacesIterators()

template<typename TKSpace , typename TCellContainer = typename TKSpace::template CellMap< CubicalCellData >::Type>

template<typename CellMapIteratorOutputIterator >

void DGtal::CubicalComplex< TKSpace, TCellContainer >::directFacesIterators	(	CellMapIteratorOutputIterator &	outIt,
		const Cell &	aCell
	)

Outputs all the iterators on cells that are direct faces of aCell with output iterator it (direct faces are lower incident cells with a dimension just one below).

Parameters

outIt	the output iterator on CellMapIterator that is used for outputing face iterators.
aCell	any cell valid in the Khalimsky space associated to the complex.

Template Parameters

CellMapIteratorOutputIterator any model of boost::OutputIterator, with value_type CellMapIterator.

Note: all returned cells belong to this complex, while it is not compulsory for aCell to belong to it.

◆ empty()

template<typename TKSpace , typename TCellContainer = typename TKSpace::template CellMap< CubicalCellData >::Type>

bool DGtal::CubicalComplex< TKSpace, TCellContainer >::empty ( ) const

Returns: 'true' if and only if the complex does not hold any cell.

◆ end() [1/4]

template<typename TKSpace , typename TCellContainer = typename TKSpace::template CellMap< CubicalCellData >::Type>

Iterator DGtal::CubicalComplex< TKSpace, TCellContainer >::end ( )

Returns: an iterator pointing after the last cell of this complex (upper dimensional cells arrive last).

◆ end() [2/4]

template<typename TKSpace , typename TCellContainer = typename TKSpace::template CellMap< CubicalCellData >::Type>

ConstIterator DGtal::CubicalComplex< TKSpace, TCellContainer >::end ( ) const

Returns: an iterator pointing after the last cell of this complex (upper dimensional cells arrive last).

Referenced by DGtal::CubicalComplex< TKSpace, TCellContainer >::ConstIterator::ConstIterator(), drawComplex(), GIVEN(), DGtal::CubicalComplex< TKSpace, TCellContainer >::Iterator::Iterator(), main(), DGtal::CubicalComplex< TKSpace, TCellContainer >::ConstIterator::nextDimension(), DGtal::CubicalComplex< TKSpace, TCellContainer >::Iterator::nextDimension(), and SCENARIO().

◆ end() [3/4]

template<typename TKSpace , typename TCellContainer = typename TKSpace::template CellMap< CubicalCellData >::Type>

CellMapIterator DGtal::CubicalComplex< TKSpace, TCellContainer >::end ( Dimension d )

Parameters

d	any valid dimension.

Returns: an iterator pointing after the last cell of dimension d of this.

◆ end() [4/4]

template<typename TKSpace , typename TCellContainer = typename TKSpace::template CellMap< CubicalCellData >::Type>

CellMapConstIterator DGtal::CubicalComplex< TKSpace, TCellContainer >::end ( Dimension d ) const

Parameters

d	any valid dimension.

Returns: a const iterator pointing after the last cell of dimension d of this.

◆ equal_range() [1/2]

template<typename TKSpace , typename TCellContainer = typename TKSpace::template CellMap< CubicalCellData >::Type>

std::pair< Iterator, Iterator > DGtal::CubicalComplex< TKSpace, TCellContainer >::equal_range ( const Cell & aCell )

Get range of equal elements to aCell. Because all elements in a set container are unique, the range returned will contain a single element at most.

Parameters

aCell any cell.

Returns: the bounds of a range that includes all the elements in the container that are equivalent to val.

◆ equal_range() [2/2]

template<typename TKSpace , typename TCellContainer = typename TKSpace::template CellMap< CubicalCellData >::Type>

std::pair< ConstIterator, ConstIterator > DGtal::CubicalComplex< TKSpace, TCellContainer >::equal_range ( const Cell & aCell ) const

Get range of equal elements to aCell. Because all elements in a set container are unique, the range returned will contain a single element at most.

Parameters

aCell any cell.

Returns: the bounds of a range that includes all the elements in the container that are equivalent to val.

◆ erase() [1/3]

template<typename TKSpace , typename TCellContainer = typename TKSpace::template CellMap< CubicalCellData >::Type>

Size DGtal::CubicalComplex< TKSpace, TCellContainer >::erase ( const Cell & aCell )

Erases cell aCell from the complex (STL version, see eraseCell).

Parameters

aCell any cell valid in the Khalimsky space associated to the complex.

Returns: the number of cells effectively removed from the cubical complex.

◆ erase() [2/3]

template<typename TKSpace , typename TCellContainer = typename TKSpace::template CellMap< CubicalCellData >::Type>

void DGtal::CubicalComplex< TKSpace, TCellContainer >::erase	(	Iterator	first,
		Iterator	last
	)

Erases range of cells [first, last ).

Parameters

first	an iterator on the beginning of a range of cells within this complex.
last	an iterator on the end of a range of cells within this complex.

◆ erase() [3/3]

template<typename TKSpace , typename TCellContainer = typename TKSpace::template CellMap< CubicalCellData >::Type>

void DGtal::CubicalComplex< TKSpace, TCellContainer >::erase ( Iterator position )

Erase element pointed by iterator it.

Parameters

position any iterator on a valid cell.

◆ eraseCell() [1/3]

template<typename TKSpace , typename TCellContainer = typename TKSpace::template CellMap< CubicalCellData >::Type>

void DGtal::CubicalComplex< TKSpace, TCellContainer >::eraseCell ( CellMapIterator it )

Erases cell pointed by iterator it.

Parameters

it	any valid iterator on a cell of this complex.

◆ eraseCell() [2/3]

template<typename TKSpace , typename TCellContainer = typename TKSpace::template CellMap< CubicalCellData >::Type>

Size DGtal::CubicalComplex< TKSpace, TCellContainer >::eraseCell ( const Cell & aCell )

Erases cell aCell from the complex.

Parameters

aCell any cell valid in the Khalimsky space associated to the complex.

Returns: the number of cells effectively removed from the cubical complex.

◆ eraseCell() [3/3]

template<typename TKSpace , typename TCellContainer = typename TKSpace::template CellMap< CubicalCellData >::Type>

Size DGtal::CubicalComplex< TKSpace, TCellContainer >::eraseCell	(	Dimension	d,
		const Cell &	aCell
	)

Erases cell aCell from the complex.

Parameters

d	the dimension of cell aCell.
aCell	any cell valid in the Khalimsky space associated to the complex.

Returns: the number of cells effectively removed from the cubical complex.

◆ eraseCells() [1/3]

template<typename TKSpace , typename TCellContainer = typename TKSpace::template CellMap< CubicalCellData >::Type>

template<typename CellConstIterator >

Size DGtal::CubicalComplex< TKSpace, TCellContainer >::eraseCells	(	CellConstIterator	it,
		CellConstIterator	itE
	)

Erases the cells stored in range [it,itE) from the CubicalComplex.

Parameters

it	an iterator pointing at the beginning of a range of (arbitrary) cells.
itE	an iterator pointing after the end of a range of (arbitrary) cells.

Returns: the number of cells effectively removed from the cubical complex.

Template Parameters

CellConstIterator any model of a forward const iterator on Cell.

◆ eraseCells() [2/3]

template<typename TKSpace , typename TCellContainer = typename TKSpace::template CellMap< CubicalCellData >::Type>

void DGtal::CubicalComplex< TKSpace, TCellContainer >::eraseCells	(	CellMapIterator	it,
		CellMapIterator	itE
	)

Erases cells in range [it, itE).

Parameters

it	any valid iterator on the first element of range of cells of this complex.
itE	any valid iterator after the last element of range of cells of this complex.

◆ eraseCells() [3/3]

template<typename TKSpace , typename TCellContainer = typename TKSpace::template CellMap< CubicalCellData >::Type>

template<typename CellConstIterator >

Size DGtal::CubicalComplex< TKSpace, TCellContainer >::eraseCells	(	Dimension	d,
		CellConstIterator	it,
		CellConstIterator	itE
	)

Erases the cells of dimension d stored in range [it,itE) from the CubicalComplex.

Parameters

d	the dimension of every cell in range [it,itE).
it	an iterator pointing at the beginning of a range of (arbitrary) cells.
itE	an iterator pointing after the end of a range of (arbitrary) cells.

Returns: the number of cells effectively removed from the cubical complex.

Template Parameters

CellConstIterator any model of a forward const iterator on Cell.

◆ euler()

template<typename TKSpace , typename TCellContainer = typename TKSpace::template CellMap< CubicalCellData >::Type>

Integer DGtal::CubicalComplex< TKSpace, TCellContainer >::euler ( ) const

Note: For instance, all Platonician solids have euler number equal to one, while their surface have euler number equal to two.

Returns: the Euler number of this complex which equals nbCells( 0 ) - nbCells( 1 ) + nbCells( 2 ) - ...

Referenced by SCENARIO(), and TEST_CASE().

◆ faces()

template<typename TKSpace , typename TCellContainer = typename TKSpace::template CellMap< CubicalCellData >::Type>

template<typename CellOutputIterator >

void DGtal::CubicalComplex< TKSpace, TCellContainer >::faces	(	CellOutputIterator &	outIt,
		const Cell &	aCell,
		bool	hintClosed = `false`
	)		const

Outputs all the cells that are proper faces of aCell with output iterator it.

Parameters

outIt	the output iterator on Cell that is used for outputing faces.
aCell	any cell valid in the Khalimsky space associated to the complex.
hintClosed	when 'true', this hint tells that the complex is closed, so this speeds up this method, otherwise, the complex may be arbitrary.

Template Parameters

CellOutputIterator any model of boost::OutputIterator, with value_type Cell.

Note: all returned cells belong to this complex, while it is not compulsory for aCell to belong to it.

Referenced by GIVEN().

◆ fillData() [1/2]

template<typename TKSpace , typename TCellContainer = typename TKSpace::template CellMap< CubicalCellData >::Type>

void DGtal::CubicalComplex< TKSpace, TCellContainer >::fillData ( Data data = Data() )

Fills the data of every cell of this cubical complex, which becomes data. Default value resets the data to zero.

Parameters

data any data.

◆ fillData() [2/2]

template<typename TKSpace , typename TCellContainer = typename TKSpace::template CellMap< CubicalCellData >::Type>

void DGtal::CubicalComplex< TKSpace, TCellContainer >::fillData	(	Dimension	d,
		Data	data = `Data()`
	)

Fills the data of every cell of dimension d this cubical complex, which becomes data. Default value resets the data to zero.

Parameters

d	the dimension of cell aCell.
data	any data.

◆ find() [1/2]

template<typename TKSpace , typename TCellContainer = typename TKSpace::template CellMap< CubicalCellData >::Type>

Iterator DGtal::CubicalComplex< TKSpace, TCellContainer >::find ( const Cell & aCell )

Parameters

aCell any cell valid in the Khalimsky space associated to the complex.

Returns: an iterator pointing on the cell or end() if not found.

◆ find() [2/2]

template<typename TKSpace , typename TCellContainer = typename TKSpace::template CellMap< CubicalCellData >::Type>

ConstIterator DGtal::CubicalComplex< TKSpace, TCellContainer >::find ( const Cell & aCell ) const

Parameters

aCell any cell valid in the Khalimsky space associated to the complex.

Returns: an iterator pointing on the cell or end() if not found.

◆ findCell() [1/4]

template<typename TKSpace , typename TCellContainer = typename TKSpace::template CellMap< CubicalCellData >::Type>

CellMapIterator DGtal::CubicalComplex< TKSpace, TCellContainer >::findCell ( const Cell & aCell )

Parameters

aCell any cell valid in the Khalimsky space associated to the complex.

Returns: an iterator pointing on the pair (aCell,data) if the cell belongs to the complex, or end( dim( aCell ) )

◆ findCell() [2/4]

template<typename TKSpace , typename TCellContainer = typename TKSpace::template CellMap< CubicalCellData >::Type>

CellMapConstIterator DGtal::CubicalComplex< TKSpace, TCellContainer >::findCell ( const Cell & aCell ) const

Parameters

aCell any cell valid in the Khalimsky space associated to the complex.

Returns: an iterator pointing on the pair (aCell,data) if the cell belongs to the complex, or end( dim( aCell ) )

Referenced by SCENARIO().

◆ findCell() [3/4]

template<typename TKSpace , typename TCellContainer = typename TKSpace::template CellMap< CubicalCellData >::Type>

CellMapIterator DGtal::CubicalComplex< TKSpace, TCellContainer >::findCell	(	Dimension	d,
		const Cell &	aCell
	)

Parameters

d	the dimension of cell aCell.
aCell	any cell valid in the Khalimsky space associated to the complex.

Returns: an iterator pointing on the pair (aCell,data) if the cell belongs to the complex, or end( d )

◆ findCell() [4/4]

template<typename TKSpace , typename TCellContainer = typename TKSpace::template CellMap< CubicalCellData >::Type>

CellMapConstIterator DGtal::CubicalComplex< TKSpace, TCellContainer >::findCell	(	Dimension	d,
		const Cell &	aCell
	)		const

Parameters

d	the dimension of cell aCell.
aCell	any cell valid in the Khalimsky space associated to the complex.

Returns: an iterator pointing on the pair (aCell,data) if the cell belongs to the complex, or end( d )

◆ getCells() [1/2]

template<typename TKSpace , typename TCellContainer = typename TKSpace::template CellMap< CubicalCellData >::Type>

CellMap & DGtal::CubicalComplex< TKSpace, TCellContainer >::getCells ( const Dimension d )

Parameters

d	input Dimension

Returns: CellContainer associated to cell of dimension d.

◆ getCells() [2/2]

template<typename TKSpace , typename TCellContainer = typename TKSpace::template CellMap< CubicalCellData >::Type>

const CellMap & DGtal::CubicalComplex< TKSpace, TCellContainer >::getCells ( const Dimension d ) const

Parameters

d	input Dimension

Returns: CellContainer associated to cell of dimension d.

◆ getInteriorAndBoundary()

template<typename TKSpace , typename TCellContainer = typename TKSpace::template CellMap< CubicalCellData >::Type>

void DGtal::CubicalComplex< TKSpace, TCellContainer >::getInteriorAndBoundary	(	CubicalComplex< TKSpace, TCellContainer > &	intcc,
		CubicalComplex< TKSpace, TCellContainer > &	bdcc,
		bool	hintClosed = `false`
	)		const

Computes the (topological) interior intcc and the (topological) boundary bdcc of this complex. Note that bdcc is not necessarily a subcomplex.

Parameters

[out]	intcc	returns the interior subcomplex of this complex.
[out]	bdcc	returns the boundary of this complex.
	hintClosed	when 'true', this hint tells that the complex is closed, so this speeds up this method, otherwise, the complex may be arbitrary.

◆ insert() [1/3]

template<typename TKSpace , typename TCellContainer = typename TKSpace::template CellMap< CubicalCellData >::Type>

std::pair< Iterator, bool > DGtal::CubicalComplex< TKSpace, TCellContainer >::insert ( const Cell & aCell )

Insert element aCell into the complex.

Parameters

aCell any cell valid in the Khalimsky space associated to the complex.

Returns: a pair with an iterator pointing on the inserted element and a boolean that is true whenever this was indeed a new element in the complex.

Referenced by SCENARIO().

◆ insert() [2/3]

template<typename TKSpace , typename TCellContainer = typename TKSpace::template CellMap< CubicalCellData >::Type>

template<class InputIterator >

void DGtal::CubicalComplex< TKSpace, TCellContainer >::insert	(	InputIterator	first,
		InputIterator	last
	)

Insert a range of cells [first, last).

Template Parameters

InputIterator any model of boost::InputIterator where elements are Cell.

Parameters

first	the beginning of the range.
last	the end of the range.

◆ insert() [3/3]

template<typename TKSpace , typename TCellContainer = typename TKSpace::template CellMap< CubicalCellData >::Type>

Iterator DGtal::CubicalComplex< TKSpace, TCellContainer >::insert	(	Iterator	position,
		const Cell &	aCell
	)

Insert element aCell into the complex with possible hint given by position.

Parameters

aCell	any cell valid in the Khalimsky space associated to the complex.
position	an hint for the position where the element can be inserted.

Returns: an iterator pointing on the inserted element.

◆ insertCell() [1/2]

template<typename TKSpace , typename TCellContainer = typename TKSpace::template CellMap< CubicalCellData >::Type>

void DGtal::CubicalComplex< TKSpace, TCellContainer >::insertCell	(	const Cell &	aCell,
		const Data &	data = `Data()`
	)

Insert cell aCell into CubicalComplex and assign to it the value data.

Parameters

aCell	any cell valid in the Khalimsky space associated to the complex.
data	any value.

Referenced by GIVEN(), main(), and SCENARIO().

◆ insertCell() [2/2]

template<typename TKSpace , typename TCellContainer = typename TKSpace::template CellMap< CubicalCellData >::Type>

void DGtal::CubicalComplex< TKSpace, TCellContainer >::insertCell	(	Dimension	d,
		const Cell &	aCell,
		const Data &	data = `Data()`
	)

Insert cell aCell into CubicalComplex and assign to it the value data. Faster than the other insertCell method.

Parameters

d	the dimension of cell aCell.
aCell	any cell valid in the Khalimsky space associated to the complex.
data	any value.

◆ insertCells() [1/2]

template<typename TKSpace , typename TCellContainer = typename TKSpace::template CellMap< CubicalCellData >::Type>

template<typename CellConstIterator >

void DGtal::CubicalComplex< TKSpace, TCellContainer >::insertCells	(	CellConstIterator	it,
		CellConstIterator	itE,
		const Data &	data = `Data()`
	)

Insert the cells within range [it,itE) into the CubicalComplex. The value associated to each cell is the default.

Parameters

it	an iterator pointing at the beginning of a range of (arbitrary) cells.
itE	an iterator pointing after the end of a range of (arbitrary) cells.
data	any value.

Template Parameters

CellConstIterator any model of a forward const iterator on Cell.

◆ insertCells() [2/2]

template<typename TKSpace , typename TCellContainer = typename TKSpace::template CellMap< CubicalCellData >::Type>

template<typename CellConstIterator >

void DGtal::CubicalComplex< TKSpace, TCellContainer >::insertCells	(	Dimension	d,
		CellConstIterator	it,
		CellConstIterator	itE,
		const Data &	data = `Data()`
	)

Insert the cells within range [it,itE) into the CubicalComplex. The value associated to each cell is the default.

Parameters

d	the dimension of all cells in the range [it,itE).
it	an iterator pointing at the beginning of a range of (arbitrary) cells.
itE	an iterator pointing after the end of a range of (arbitrary) cells.
data	any value.

Template Parameters

CellConstIterator any model of a forward const iterator on Cell.

◆ interior()

template<typename TKSpace , typename TCellContainer = typename TKSpace::template CellMap< CubicalCellData >::Type>

CubicalComplex DGtal::CubicalComplex< TKSpace, TCellContainer >::interior ( ) const

Computes the (topological) interior to this complex.

Returns: the subcomplex of this composed of its interior cells.

Referenced by main().

◆ isCellBoundary()

template<typename TKSpace , typename TCellContainer = typename TKSpace::template CellMap< CubicalCellData >::Type>

bool DGtal::CubicalComplex< TKSpace, TCellContainer >::isCellBoundary ( const Cell & aCell ) const

Parameters

aCell any cell valid in the Khalimsky space associated to the complex.

Returns: 'true' if and only if aCell is not interior to the complex, which means that it has more co-faces in the Khalimsky space than in this complex.

◆ isCellInterior()

template<typename TKSpace , typename TCellContainer = typename TKSpace::template CellMap< CubicalCellData >::Type>

bool DGtal::CubicalComplex< TKSpace, TCellContainer >::isCellInterior ( const Cell & aCell ) const

Parameters

aCell any cell valid in the Khalimsky space associated to the complex.

Returns: 'true' if and only if aCell is interior to the complex, which means that it has the same co-faces in the Khalimsky space as in this complex.

◆ isValid()

template<typename TKSpace , typename TCellContainer = typename TKSpace::template CellMap< CubicalCellData >::Type>

bool DGtal::CubicalComplex< TKSpace, TCellContainer >::isValid ( ) const

Checks the validity/consistency of the object.

Returns: 'true' if the object is valid, 'false' otherwise.

◆ link()

template<typename TKSpace , typename TCellContainer = typename TKSpace::template CellMap< CubicalCellData >::Type>

CubicalComplex DGtal::CubicalComplex< TKSpace, TCellContainer >::link	(	const CubicalComplex< TKSpace, TCellContainer > &	S,
		bool	hintClosed = `false`,
		bool	hintOpen = `false`
	)		const

Returns the link of the cells in S within this complex, i.e. the closed star of S minus the stars of all faces of S.

Parameters

S	any complex the cells of which belong to this complex.
hintClosed	when 'true', this hint tells that the complex is (locally around S) closed, so this speeds up this method, otherwise, the complex may be arbitrary.
hintOpen	when 'true', this hint tells that the complex is (locally around S) open, so this speeds up this method, otherwise, the complex may be arbitrary.

Returns: the link of S within this complex as a cubical complex.

Referenced by main(), and SCENARIO().

◆ max_size()

template<typename TKSpace , typename TCellContainer = typename TKSpace::template CellMap< CubicalCellData >::Type>

Size DGtal::CubicalComplex< TKSpace, TCellContainer >::max_size ( ) const

Returns: the maximal number of cells in this complex (i.e., the number of cells of the Khalimsky space).

◆ nbCells()

template<typename TKSpace , typename TCellContainer = typename TKSpace::template CellMap< CubicalCellData >::Type>

Size DGtal::CubicalComplex< TKSpace, TCellContainer >::nbCells ( Dimension d ) const

Parameters

d	the dimension of cells.

Returns: the number of cells of dimension d in this complex.

Referenced by GIVEN(), and SCENARIO().

◆ open() [1/2]

template<typename TKSpace , typename TCellContainer = typename TKSpace::template CellMap< CubicalCellData >::Type>

void DGtal::CubicalComplex< TKSpace, TCellContainer >::open ( )

Open the whole complex (see also DGtal::operator*).

Referenced by DGtal::operator*().

◆ open() [2/2]

template<typename TKSpace , typename TCellContainer = typename TKSpace::template CellMap< CubicalCellData >::Type>

void DGtal::CubicalComplex< TKSpace, TCellContainer >::open ( Dimension k )

Open all cells of dimension less or or equal to k.

Parameters

k	any strictly positive integer.

◆ operator()()

template<typename TKSpace , typename TCellContainer = typename TKSpace::template CellMap< CubicalCellData >::Type>

bool DGtal::CubicalComplex< TKSpace, TCellContainer >::operator() ( const Cell & aCell ) const

Makes CubicalComplex a functor Cell -> boolean, which represents the characteristic cell function.

Parameters

aCell any cell valid in the Khalimsky space associated to the complex.

Returns: 'true' if and only if aCell belongs to this complex.

◆ operator=()

template<typename TKSpace , typename TCellContainer = typename TKSpace::template CellMap< CubicalCellData >::Type>

CubicalComplex & DGtal::CubicalComplex< TKSpace, TCellContainer >::operator= ( const CubicalComplex< TKSpace, TCellContainer > & other )

Assignment.

Parameters

other the object to copy.

Returns: a reference on 'this'.

◆ operator[]()

template<typename TKSpace , typename TCellContainer = typename TKSpace::template CellMap< CubicalCellData >::Type>

Data & DGtal::CubicalComplex< TKSpace, TCellContainer >::operator[] ( const Cell & aCell )

Access or change the data associated to aCell. Note that if aCell was not in this complex, then it is inserted.

Parameters

aCell any cell valid in the Khalimsky space associated to the complex.

Returns: a reference on the data associated with aCell.

◆ selfDisplay()

template<typename TKSpace , typename TCellContainer = typename TKSpace::template CellMap< CubicalCellData >::Type>

void DGtal::CubicalComplex< TKSpace, TCellContainer >::selfDisplay ( std::ostream & out ) const

Writes/Displays the object on an output stream.

Parameters

out	the output stream where the object is written.

◆ size()

template<typename TKSpace , typename TCellContainer = typename TKSpace::template CellMap< CubicalCellData >::Type>

Size DGtal::CubicalComplex< TKSpace, TCellContainer >::size ( ) const

Returns: the total number of cells in this complex.

Referenced by SCENARIO().

◆ space()

template<typename TKSpace , typename TCellContainer = typename TKSpace::template CellMap< CubicalCellData >::Type>

const KSpace & DGtal::CubicalComplex< TKSpace, TCellContainer >::space ( ) const

Returns: a reference to the Khalimsky space associated to this complex.

Referenced by DGtal::operator!=(), DGtal::operator<=(), DGtal::operator==(), and DGtal::operator>=().

◆ star()

template<typename TKSpace , typename TCellContainer = typename TKSpace::template CellMap< CubicalCellData >::Type>

CubicalComplex DGtal::CubicalComplex< TKSpace, TCellContainer >::star	(	const CubicalComplex< TKSpace, TCellContainer > &	S,
		bool	hintOpen = `false`
	)		const

Returns the star of the cells in S within this complex, i.e. the set of all cells of this complex that have any faces in S.

Parameters

S	any complex the cells of which belong to this complex.
hintOpen	when 'true', this hint tells that the complex is (locally around S) open, so this speeds up this method, otherwise, the complex may be arbitrary.

Returns: the star of S within this complex as a cubical complex.

Referenced by main().

◆ swap()

template<typename TKSpace , typename TCellContainer = typename TKSpace::template CellMap< CubicalCellData >::Type>

void DGtal::CubicalComplex< TKSpace, TCellContainer >::swap ( CubicalComplex< TKSpace, TCellContainer > & other )

Swaps complex other with this. Note that complexes must live in the same space. If one complex is invalid then it is initialized with the space of the other.

Parameters

other a complex living in the same space.

Friends And Related Function Documentation

◆ DGtal::operator!=

template<typename TKSpace , typename TCellContainer = typename TKSpace::template CellMap< CubicalCellData >::Type>

template<typename K , typename C >

bool DGtal::operator!=	(	const CubicalComplex< K, C > &	,
		const CubicalComplex< K, C > &
	)

friend

◆ DGtal::operator&

template<typename TKSpace , typename TCellContainer = typename TKSpace::template CellMap< CubicalCellData >::Type>

template<typename K , typename C >

CubicalComplex< K, C > DGtal::operator&	(	const CubicalComplex< K, C > &	,
		const CubicalComplex< K, C > &
	)

friend

◆ DGtal::operator&=

template<typename TKSpace , typename TCellContainer = typename TKSpace::template CellMap< CubicalCellData >::Type>

template<typename K , typename C >

CubicalComplex< K, C > & DGtal::operator&=	(	CubicalComplex< K, C > &	,
		const CubicalComplex< K, C > &
	)

friend

◆ DGtal::operator*

template<typename TKSpace , typename TCellContainer = typename TKSpace::template CellMap< CubicalCellData >::Type>

template<typename K , typename C >

CubicalComplex< K, C > DGtal::operator* ( const CubicalComplex< K, C > & )

friend

◆ DGtal::operator-

template<typename TKSpace , typename TCellContainer = typename TKSpace::template CellMap< CubicalCellData >::Type>

template<typename K , typename C >

CubicalComplex< K, C > DGtal::operator-	(	const CubicalComplex< K, C > &	,
		const CubicalComplex< K, C > &
	)

friend

◆ DGtal::operator-=

template<typename TKSpace , typename TCellContainer = typename TKSpace::template CellMap< CubicalCellData >::Type>

template<typename K , typename C >

CubicalComplex< K, C > & DGtal::operator-=	(	CubicalComplex< K, C > &	,
		const CubicalComplex< K, C > &
	)

friend

◆ DGtal::operator<=

template<typename TKSpace , typename TCellContainer = typename TKSpace::template CellMap< CubicalCellData >::Type>

template<typename K , typename C >

bool DGtal::operator<=	(	const CubicalComplex< K, C > &	,
		const CubicalComplex< K, C > &
	)

friend

◆ DGtal::operator==

template<typename TKSpace , typename TCellContainer = typename TKSpace::template CellMap< CubicalCellData >::Type>

template<typename K , typename C >

bool DGtal::operator==	(	const CubicalComplex< K, C > &	,
		const CubicalComplex< K, C > &
	)

friend

◆ DGtal::operator>=

template<typename TKSpace , typename TCellContainer = typename TKSpace::template CellMap< CubicalCellData >::Type>

template<typename K , typename C >

bool DGtal::operator>=	(	const CubicalComplex< K, C > &	,
		const CubicalComplex< K, C > &
	)

friend

◆ DGtal::operator^

template<typename TKSpace , typename TCellContainer = typename TKSpace::template CellMap< CubicalCellData >::Type>

template<typename K , typename C >

CubicalComplex< K, C > DGtal::operator^	(	const CubicalComplex< K, C > &	,
		const CubicalComplex< K, C > &
	)

friend

◆ DGtal::operator^=

template<typename TKSpace , typename TCellContainer = typename TKSpace::template CellMap< CubicalCellData >::Type>

template<typename K , typename C >

CubicalComplex< K, C > & DGtal::operator^=	(	CubicalComplex< K, C > &	,
		const CubicalComplex< K, C > &
	)

friend

◆ DGtal::operator|

template<typename TKSpace , typename TCellContainer = typename TKSpace::template CellMap< CubicalCellData >::Type>

template<typename K , typename C >

CubicalComplex< K, C > DGtal::operator\|	(	const CubicalComplex< K, C > &	,
		const CubicalComplex< K, C > &
	)

friend

◆ DGtal::operator|=

template<typename TKSpace , typename TCellContainer = typename TKSpace::template CellMap< CubicalCellData >::Type>

template<typename K , typename C >

CubicalComplex< K, C > & DGtal::operator\|=	(	CubicalComplex< K, C > &	,
		const CubicalComplex< K, C > &
	)

friend

◆ DGtal::operator~

template<typename TKSpace , typename TCellContainer = typename TKSpace::template CellMap< CubicalCellData >::Type>

template<typename K , typename C >

CubicalComplex< K, C > DGtal::operator~ ( const CubicalComplex< K, C > & )

friend

Field Documentation

◆ dimension

template<typename TKSpace , typename TCellContainer = typename TKSpace::template CellMap< CubicalCellData >::Type>

const Dimension DGtal::CubicalComplex< TKSpace, TCellContainer >::dimension = KSpace::dimension

static

The dimension of the embedding space.

Definition at line 242 of file CubicalComplex.h.

Referenced by DGtal::CubicalComplex< TKSpace, TCellContainer >::ConstIterator::ConstIterator(), DGtal::CubicalComplex< TKSpace, TCellContainer >::Iterator::Iterator(), DGtal::CubicalComplex< TKSpace, TCellContainer >::ConstIterator::nextDimension(), DGtal::CubicalComplex< TKSpace, TCellContainer >::Iterator::nextDimension(), DGtal::operator!=(), DGtal::operator&(), DGtal::operator&=(), DGtal::operator-(), DGtal::operator-=(), DGtal::operator<=(), DGtal::operator==(), DGtal::operator>=(), DGtal::operator^(), DGtal::operator^=(), DGtal::operator|(), and DGtal::operator|=().

◆ myCells

template<typename TKSpace , typename TCellContainer = typename TKSpace::template CellMap< CubicalCellData >::Type>

std::vector<CellMap> DGtal::CubicalComplex< TKSpace, TCellContainer >::myCells

protected

An array of map Cell -> Data that stores cells dimension per dimension (i.e. cells of dimension 0 are stored in myCells[0], cells of dimension 1 in myCells[1] and so on).

Definition at line 1301 of file CubicalComplex.h.

Referenced by DGtal::operator!=(), DGtal::operator&(), DGtal::operator&=(), DGtal::operator-(), DGtal::operator-=(), DGtal::operator<=(), DGtal::operator==(), DGtal::operator>=(), DGtal::operator^(), DGtal::operator^=(), DGtal::operator|(), and DGtal::operator|=().

◆ myKSpace

template<typename TKSpace , typename TCellContainer = typename TKSpace::template CellMap< CubicalCellData >::Type>

const KSpace* DGtal::CubicalComplex< TKSpace, TCellContainer >::myKSpace

protected

The Khalimsky space in which lives the cubical complex.

Definition at line 1296 of file CubicalComplex.h.

The documentation for this class was generated from the following file:

CubicalComplex.h

Data Structures

Public Types

Public Member Functions

Static Public Attributes

Protected Member Functions

Protected Attributes

Friends

Detailed Description

Member Typedef Documentation

◆ Cell

◆ CellContainer

◆ CellMap

◆ CellMapConstIterator

◆ CellMapIterator

◆ Cells

◆ const_iterator

◆ const_pointer

◆ const_reference

◆ Data

◆ difference_type

◆ DirIterator

◆ Integer

◆ iterator

◆ KSpace

◆ Point

◆ pointer

◆ PreCell

◆ reference

◆ Self

◆ Size

◆ size_type

◆ Space

◆ value_type

Member Enumeration Documentation

◆ CellType

Constructor & Destructor Documentation

◆ ~CubicalComplex()

◆ CubicalComplex() [1/3]

◆ CubicalComplex() [2/3]

◆ CubicalComplex() [3/3]

Member Function Documentation

◆ begin() [1/4]

◆ begin() [2/4]

◆ begin() [3/4]

◆ begin() [4/4]

◆ belongs() [1/4]

◆ belongs() [2/4]

◆ belongs() [3/4]

◆ belongs() [4/4]

◆ BOOST_CONCEPT_ASSERT() [1/2]

◆ BOOST_CONCEPT_ASSERT() [2/2]

◆ BOOST_STATIC_ASSERT() [1/3]

◆ BOOST_STATIC_ASSERT() [2/3]

◆ BOOST_STATIC_ASSERT() [3/3]

◆ BOOST_STATIC_CONSTANT() [1/5]

◆ BOOST_STATIC_CONSTANT() [2/5]

◆ BOOST_STATIC_CONSTANT() [3/5]

◆ BOOST_STATIC_CONSTANT() [4/5]

◆ BOOST_STATIC_CONSTANT() [5/5]

◆ boundary()

◆ cellBoundary()

◆ cellCoBoundary()

◆ className()

◆ clear() [1/2]

◆ clear() [2/2]

◆ close() [1/2]

◆ close() [2/2]

◆ closure()

◆ coFaces()

◆ computeCellType()

◆ construct()

◆ count()

◆ dim() [1/2]

◆ dim() [2/2]

◆ directCoFaces()

◆ directCoFacesIterators()

◆ directFaces()

◆ directFacesIterators()

◆ empty()

◆ end() [1/4]